Simplify estimate gaussian covariances diag (scikit-learn#30414)

Co-authored-by: mekleo <[email protected]>

Author: ogrisel

doc/whats_new/upcoming_changes/sklearn.mixture/30414.efficiency.rst

@@ -0,0 +1,4 @@
+- Simplified redundant computation when estimating covariances in
+  :class:`~mixture.GaussianMixture` with a `covariance_type="spherical"` or
+  `covariance_type="diag"`.
+  By :user:`Leonce Mekinda <mekleo>` and :user:`Olivier Grisel <ogrisel>`

sklearn/mixture/_gaussian_mixture.py

@@ -228,8 +228,7 @@ def _estimate_gaussian_covariances_diag(resp, X, nk, means, reg_covar):
     """
     avg_X2 = np.dot(resp.T, X * X) / nk[:, np.newaxis]
     avg_means2 = means**2
-    avg_X_means = means * np.dot(resp.T, X) / nk[:, np.newaxis]
-    return avg_X2 - 2 * avg_X_means + avg_means2 + reg_covar
+    return avg_X2 - avg_means2 + reg_covar
 
 
 def _estimate_gaussian_covariances_spherical(resp, X, nk, means, reg_covar):